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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Condensing Logarithmic Expressions In Exercises 63-66, use the properties of logarithms to rewrite the expression as the logarithm of a single quantity. (Assume all variables are positive.)

1 3 ln ( y 2 6 ) 2 ln ( 3 z + 2 )

To determine

To calculate: The reduced expression of the expression 13ln(y26)2ln(3z+2) using the properties of logarithms.

Explanation

Given Information:

The provided expression is 13ln(y26)2ln(3z+2).

Formula used:

The property of logarithms for the expression lnxn is lnxn=nlnx where x and y are real numbers greater than 0.

The property of logarithms for the expression ln(xy) is ln(xy)=lnxlny where x and y are real numbers greater than 0.

Calculation:

Consider the expression, 13ln(y26)2ln(3z+2)

Apply the property of lnxn in the above expression as,

13ln(y26)2ln(3z+2)=ln(y26)13ln<

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